The home side had the advantage of a very strong wind in the first half and made maximum use of it to scorch into an 0-5 to 0-1 lead after 10 minutes, senior substitute Conor Brosnan scoring three of his side's points.
With Liam Dennehy also showing well for the Leesiders at full-forward, Cork looked like winning this game in a canter.
However, Limerick improved greatly after Alan Kitson was moved to centre-forward, and they had the deficit down to two points after 20 minutes, mainly through the accuracy of Mark Culhane from frees which a hesistant Cork defence gave away far too easy.
Cork created a great goal chance late in the in the opening half but keeper John Kiely was in magnificent form, denying Kieran Daly with a point blank save.
The Shannonsiders also spurned a goal chance just before half time when their captain Tom Kilroy blazed wide with only the goalkeeper to beat.
Half-time arrived with Cork 0-9 to 0-6 in front, and given the strength of the wind, it didn't look to be enough.
By the end of the third quarter the deficit was down to the minimum after Mark Culhane pointed twice, and only some great defending by the Wiseman brothers Donagh and Enda, prevented the home side from falling behind.
Part of Cork's problems were at midfield and the selectors took off Mark Kelleher and Seamus O'Sullivan and moved Ger Spillane and Kieran Murphy out.
Those moves work well with Spillane using his strength to power forward as every opportunity and Cork finally opened their second half account with a Conor Brosnan point in the 50th minute.
Surprisingly Limerick couldn't respond despite the wind advantage and it took another marvellous fingertip save by goalkeeper John Kiely to deny substitute Michael Kearney a goal.
Despite their dominance the Cork attack continued to waste chances, kicking five wides on the trot, before Kieran Daly finally found the target with a point in the 63rd minute to easy his side into the semi-finals later in the month.
Scorers for Cork: C. Brosnan 0-4 (0-3 frees); L. Dennehy 0-3; K. O'Sullivan 0-3 (0-1 45); K. Daly 0-1.
Limerick: M. Culhane 0-7 (0-6 frees); A. Kitson 0-1.
CORK: B. Morgan; D. Duggan, D. Wiseman, J. Honohan; M. Prout, G. Spillane, E. Wiseman; M. Kelleher, S. O'Sullivan; K. Murphy, B. Coleman, K. Daly; C. Brosnan, L. Dennehy, K. O'Sullivan.
Subs. E. O'Connor for S. O'Sullivan; M. Kearney for M. Kelleher.
LIMERICK: J. Kiely; D. Bourke, D. Dineen, A. O'Rahilly; D. Stapleton, T. McLoughlin, D. Galvin; G. Walsh, D. Horan; A. Kitson, D. Phelan, B.
Slattery; M. Culhane, T. Kilroy, K. Hartnett. Subs. J. Sheehan for Horan; A.
McEntee for Bourke; R. Lynch for Hartnett; D. Fitzgerald for Kilroy.
Referee: P. Sheehy (Kerry).